Electron-Pair Distribution in Chemical Bond Formation

Mutual Information in Conjugate Spaces for Neutral Atoms and Ions

The discrepancy among one-electron and two-electron densities for diverse N-electron atomss, enclosing neutral systems (with nuclear charge Z=N) and charge-one ions (|N−Z|=1), is quantified by means of mutual information, I, and Quantum Similarity Index, QSI, in the conjugate spaces position/momentum. These differences can be interpreted as a measure of the electron correlation of the system. The analysis is carried out by considering systems with a nuclear charge up to Z=103 and singly charged ions (cations and anions) as far as N=54. The interelectronic correlation, for any given system, is quantified through the comparison of its double-variable electron pair density and the product of the respective one-particle densities. An in-depth study along the Periodic Table reveals the importance, far beyond the weight of the systems considered, of their shell structure.

Measuring correlated electron motion in atoms with the momentum-balance density

Three new measures of relative electron motion are introduced: equimomentum, antimomentum, and momentum-balance. The equimomentum is the probability that two electrons have the exact same momentum, whereas the antimomentum is the probability that their momenta are the exact opposite. Momentum-balance (MB) is the difference between the equimomentum and antimomentum and, therefore, indicates if equal or opposite momentum is more probable in a system of electrons. The equimomentum, antimomentum, and MB densities are also introduced, which are the local contribution to each quantity. The MB and MB density of the extrapolated-full configuration interaction wave functions of atoms of the first three rows of the periodic table are analyzed, with a particular focus on contrasting the correlated motion of electrons with opposite-spin and parallel-spin. Coulomb correlation between opposite-spin electrons leads to a higher probability of equimomentum, whereas Fermi correlation between parallel-spin electrons leads to a higher probability of antimomentum. The local contribution to MB, given an electron is present, is a minimum at the nucleus and generally increases as the distance from the nucleus increases. There are also interesting similarities between the effects of Fermi correlation and Coulomb correlation (of opposite-spin electrons) on MB.

Ca2+ mediated mechanism of octa-brominated dioxin/furan formation via BDE-209 thermolysis: Introducing the Mayer bond order difference

Polybrominated dibenzo-p-dioxins/dibenzofurans (PBDD/Fs) that form during industrial thermal processes, such as the cement kiln co-processing of BDE-209, are highly toxic contaminants. Nevertheless, the formation mechanisms of octa-brominated dioxins/furans (OBDD/Fs), most PBDD/F congeners, and one precursor of the more toxic lower PBDD/Fs from BDE-209 have received little attention. In cement kiln co-processes, the Ca²⁺-mediated regulation of OBDD/F formation is still debated. In this study, simulation experiments revealed that the average brominating degree of PBDD/Fs was 7.8, indicating that OBDD/Fs are dominant congeners (93.6 % median). Density functional theory (DFT) calculations found a new transition state (TS1) with a lower energy barrier than that found in a previous study. Three major OBDD/F formation reactions suggested that the presence of Ca²⁺ was thermodynamically beneficial to the formation of OBDD/Fs. This promotion effect can be attributed to the transfer of electron density leading to a change in the Mayer bond order (MBO) among elements when Ca²⁺ was bound. Intriguingly, in the transition state structures of the Ca²⁺-bound and Ca²⁺-free systems, the MBO difference among the old and new bonds can reveal the difficulty of Ca²⁺-mediated OBDD/F formation reactions from BDE-209.